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Spectrum value for coalitional games

Mikel Álvarez-Mozos, Ziv Hellman () and Eyal Winter ()

Games and Economic Behavior, 2013, vol. 82, issue C, 132-142

Abstract: Assuming a ‘spectrum’ or ordering of the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally asymmetric power index in which positioning along the spectrum is critical. We present both a characterization of this value by means of properties and combinatoric formulae for calculating it. In simple majority games, the greatest power accrues to ‘moderate’ players who are located neither at the extremes of the spectrum nor in its center. In supermajority games, power increasingly accrues towards the extremes, and in unanimity games all power is held by the players at the extreme of the spectrum.

Keywords: Coalitional games; Shapley value; Restricted cooperation; Political spectrum (search for similar items in EconPapers)
JEL-codes: C71 D46 D72 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:82:y:2013:i:c:p:132-142

DOI: 10.1016/j.geb.2013.06.011

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